Finite Group Databasebeta

← #7205833

Subgroups — #7205833

Order 512.

1660 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53016C211yesmaximal, characteristic, complemented
2#35995C211yesmaximal, characteristic, complemented
3#32966C211yesmaximal, characteristic, complemented
4#32917C211yesmaximal, characteristic, complemented
5#32754C211yesmaximal, characteristic, complemented
6#32735C211yesmaximal, characteristic, complemented
7#31834C211yesmaximal, characteristic, complemented
8#31534C211yesmaximal, characteristic, complemented
9#31470C211yesmaximal, characteristic, complemented
10#31238C211yesmaximal, characteristic, complemented
11#31162C211yesmaximal, characteristic, complemented
12#31040C211yesmaximal, characteristic, complemented
13#30988C211yesmaximal, characteristic, complemented
14#30911C211yesmaximal, characteristic, complemented
15#30851C211yesmaximal, characteristic, complemented
16#30629C211yesmaximal, characteristic, complemented
17#30519C211yesmaximal, characteristic, complemented
18#30396C211yesmaximal, characteristic, complemented
19#27339C211yesmaximal, characteristic, complemented
20#27173C211yesmaximal, characteristic, complemented
21#26929C211yesmaximal, characteristic, complemented
22#26905C211yesmaximal, characteristic, complemented
23#26785C211yesmaximal, characteristic, complemented
24#26600C211yesmaximal, characteristic, complemented
25#26526C211yesmaximal, characteristic, complemented
26#26410C211yesmaximal, characteristic, complemented
27#25535C211yesmaximal, characteristic, complemented
28#25322C211yesmaximal, characteristic, complemented
29#25200C211yesmaximal, characteristic, complemented
30#24136C211yesmaximal, characteristic, complemented
31#23315C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#484C2211yescharacteristic, complemented
36C2×#480C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#478C2211yescharacteristic, complemented
40C2×#466C2211yescharacteristic
41C2×#465C2211yescharacteristic, complemented
42C2×#460C2211yescharacteristic
43C2×#463C2211yescharacteristic
44C2×#463C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#442C2211yescharacteristic, complemented
48#2841—21no—
49#2837—21no—
50#2820—21no—
51#2814—21no—
52#2768—21no—
53#2701—21no—
54#2694—21no—
55#2672—21no—
56#2636—21no—
57#2629C2211yescharacteristic
58#2624C2211yescharacteristic
59#2620C2211yescharacteristic
60#2603—21no—
61#2567C2211yescharacteristic, complemented
62#2552C2211yescharacteristic, complemented
63#2537C2211yescharacteristic
64#2535—21no—
65#2501C2211yescharacteristic, complemented
66#2491C2211yescharacteristic
67#2489C2211yescharacteristic, complemented
68#2454C2211yescharacteristic
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic, complemented
71#2447C2211yescharacteristic, complemented
72#2440C2211yescharacteristic, complemented
73#2433C2211yescharacteristic
74#2428C2211yescharacteristic
75#2428C2211yescharacteristic
76#2426C2211yescharacteristic, complemented
77#2424—21no—
78#2424—21no—
79#2423C2211yescharacteristic
80#2418—21no—
81#2418—21no—
82#2417C2211yescharacteristic
83#2408C2211yescharacteristic
84#2397—21no—
85#2395C2211yescharacteristic
86#2366C2211yescharacteristic
87#2366C2211yescharacteristic
88#2361C2211yescharacteristic
89#2361C2211yescharacteristic
90#2346C2211yescharacteristic
91#2100C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2093C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2075C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic, complemented
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2041C2211yescharacteristic
120#2036C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic, complemented
126#2026C2211yescharacteristic, complemented
127#2025C2211yescharacteristic, complemented
128#2023C2211yescharacteristic
129#2014C2211yescharacteristic
130#2012C2211yescharacteristic, complemented
131#2011C2211yescharacteristic
132#2011C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#1999C2211yescharacteristic
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic, complemented
139#1992C2211yescharacteristic, complemented
140#1987C2211yescharacteristic, complemented
141#1982C2211yescharacteristic
142#1973C2211yescharacteristic
143#1970C2211yescharacteristic
144#1968C2211yescharacteristic
145#1957C2211yescharacteristic
146#1955C2211yescharacteristic
147#1947C2211yescharacteristic, complemented
148#1942C2211yescharacteristic, complemented
149#1939C2211yescharacteristic, complemented
150#1939C2211yescharacteristic, complemented
151#1936C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1925C2211yescharacteristic
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1923C2211yescharacteristic
158#1923C2211yescharacteristic
159#1923C2211yescharacteristic, complemented
160#1923C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1893C2211yescharacteristic
166#1880C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic, complemented
174#1875C2211yescharacteristic
175#1874C2211yescharacteristic
176#1874C2211yescharacteristic, complemented
177#1874C2211yescharacteristic, complemented
178#1873C2211yescharacteristic
179#1869C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1853C2211yescharacteristic, complemented
189#1850C2211yescharacteristic, complemented
190#1850C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1802C2211yescharacteristic, complemented
196#1798C2211yescharacteristic
197#1798C2211yescharacteristic
198#1786C2211yescharacteristic
199#1786C2211yescharacteristic
200C4×#107C2211yescharacteristic, complemented
201C4×#103C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211#553—42no—
212#553—42no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241#518—42no—
242#518—42no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264#486—42no—
265#484—42no—
266#480—42no—
267#478—42no—
268#478—42no—
269#478—42no—
270#466—42no—
271#465—42no—
272#463—42no—
273#463—42no—
274#460—42no—
275#450—42no—
276#447—42no—
277#442—42no—
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400D411yescharacteristic
335#399—21no—
336#399—21no—
337#399—21no—
338#399—21no—
339#399—21no—
340#399—21no—
341#399—21no—
342#399D411yescharacteristic
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398D411yescharacteristic
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397D411yescharacteristic
356#397D411yescharacteristic
357#397D411yescharacteristic
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#396—21no—
366#396—21no—
367#395—21no—
368#395—21no—
369#395—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394D411yescharacteristic
382#394D411yescharacteristic
383#393—21no—
384#392—21no—
385#392—21no—
386#392—21no—
387#392—21no—
388#392—21no—
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#390—21no—
393#390—21no—
394#390—21no—
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#389—21no—
405#389—21no—
406#389—21no—
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#387—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#384C2311yescharacteristic
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#384C2311yescharacteristic
444#382—21no—
445#382—21no—
446#381—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465#376—21no—
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562#127—22no—
563#127—22no—
564#127—41no—
565#127—41no—
566#126—44no—
567#125—22no—
568#125—41no—
569#125—41no—
570#125—41no—
571#125—82no—
572#124—41no—
573#124—41no—
574#124—82no—
575#123—44no—
576#123—82no—
577#123—82no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—82no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—44no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—82no—
597#121—82no—
598#121—82no—
599#120—82no—
600#120—82no—
601#120—82no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—44no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—82no—
622C4×D4—82no—
623C4×D4—82no—
624C4×D4—82no—
625#117—22no—
626#117—22no—
627#117—41no—
628#117—41no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—44no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738#107—22no—
739#107—22no—
740#107—41no—
741#107—41no—
742#107—41no—
743#107—41no—
744#107—41no—
745#106—22no—
746#106—22no—
747#106—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755#103—22no—
756#103—22no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790#97—41no—
791C4×C8—41no—
792C4×C8—41no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×Q8—81no—
846C2×D4—22no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4H(5,𝔽2)12yes—
909C2×D42−1+412yes—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C2511yescharacteristic
971SD16—82no—
972SD16—82no—
973SD16—82no—
974D8—44no—
975D8—82no—
976D8—82no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—82no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4H(5,𝔽2)12yes—
1056C4⋊C4H(5,𝔽2)12yes—
1057C22⋊C4—24no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C42—24no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—81no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—22no—
1130C23—21no—
1131C23—22no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—48no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23—162no—
1167C23—162no—
1168C23—162no—
1169C23#57612yes—
1170C23C23×D411yescharacteristic
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—162no—
1176D4—22no—
1177D4—22no—
1178D4—22no—
1179D4—22no—
1180D4—48no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—84no—
1194D4—84no—
1195D4—82no—
1196D4—84no—
1197D4—84no—
1198D4—84no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202D4—162no—
1203D4—162no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4#57612yes—
1291C2×C4#57712yes—
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4C2×H(5,𝔽2)11yescharacteristic
1295C2×C4C2×2−1+411yescharacteristic
1296C2×C4#58511yescharacteristic
1297C2×C4#58511yescharacteristic
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C8—41no—
1305C8—41no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—42no—
1316C22—41no—
1317C22—41no—
1318C22—42no—
1319C22—42no—
1320C22—41no—
1321C22—42no—
1322C22—41no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—168no—
1349C22#348411yescharacteristic
1350C22#348811yescharacteristic
1351C22#348911yescharacteristic
1352C22C2×#57611yescharacteristic
1353C22C2×#57611yescharacteristic
1354C22C2×#57711yescharacteristic
1355C22#358611yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—41no—
1368C4—42no—
1369C4—41no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4—81no—
1379C4—81no—
1380C4#352911yescharacteristic
1381C4#353611yescharacteristic
1382C4#354111yescharacteristic
1383C4#354211yescharacteristic
1384C2—42no—
1385C2—81no—
1386C2—82no—
1387C2—82no—
1388C2—161no—
1389C2—161no—
1390C2#4545111yescharacteristic
1391C2#6162411yescharacteristic
1392C2#6166811yescharacteristic
1393C2#6200811yescharacteristic
1394C2#6205111yescharacteristic
1395C2#6215511yescharacteristic
1396C2#6220011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #53016C2semidirect
2. #35995C2semidirect
3. #32966C2semidirect
4. #32917C2semidirect
5. #32754C2semidirect
6. #32735C2semidirect
7. #31834C2semidirect
8. #31534C2semidirect
9. #31470C2semidirect
10. #31238C2semidirect
11. #31162C2semidirect
12. #31040C2semidirect
13. #30988C2semidirect
14. #30911C2semidirect
15. #30851C2semidirect
16. #30629C2semidirect
17. #30519C2semidirect
18. #30396C2semidirect
19. #27339C2semidirect
20. #27173C2semidirect
21. #26929C2semidirect
22. #26905C2semidirect
23. #26785C2semidirect
24. #26600C2semidirect
25. #26526C2semidirect
26. #26410C2semidirect
27. #25535C2semidirect
28. #25322C2semidirect
29. #25200C2semidirect
30. #24136C2semidirect
31. #23315C2semidirect
35. C2×#484C22semidirect
39. C2×#478C22semidirect
41. C2×#465C22semidirect
47. C2×#442C22semidirect
61. #2567C22semidirect
62. #2552C22semidirect
65. #2501C22semidirect
67. #2489C22semidirect
70. #2454C22semidirect
71. #2447C22semidirect
72. #2440C22semidirect
76. #2426C22semidirect
91. #2100C22semidirect
92. #2099C22semidirect
94. #2093C22semidirect
95. #2088C22semidirect
96. #2087C22semidirect
97. #2083C22semidirect
102. #2071C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
110. #2065C22semidirect
111. #2059C22semidirect
112. #2059C22semidirect
113. #2057C22semidirect
115. #2055C22semidirect
117. #2054C22semidirect
118. #2042C22semidirect
125. #2033C22semidirect
126. #2026C22semidirect
127. #2025C22semidirect
130. #2012C22semidirect
138. #1999C22semidirect
139. #1992C22semidirect
140. #1987C22semidirect
147. #1947C22semidirect
148. #1942C22semidirect
149. #1939C22semidirect
150. #1939C22semidirect
152. #1934C22semidirect
153. #1927C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
159. #1923C22semidirect
160. #1923C22semidirect
161. #1920C22semidirect
162. #1920C22semidirect
163. #1917C22semidirect
164. #1917C22semidirect
173. #1877C22semidirect
176. #1874C22semidirect
177. #1874C22semidirect
182. #1863C22semidirect
185. #1862C22semidirect
188. #1853C22semidirect
189. #1850C22semidirect
190. #1850C22semidirect
195. #1802C22semidirect
200. C4×#107C22semidirect
201. C4×#103C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#530162
#359952
#329662
#329172
#327542
#327352
#318342
#315342
#314702
#312382
#311622
#310402
#309882
#309112
#308512
#306292
#305192
#303962
#273392
#271732
#269292
#269052
#267852
#266002
#265262
#264102
#255352
#253222
#252002
#241362
#233152